Definitely Tales of Symphonia.

At the very least you need the following:

Resident Evil REmake
Tales of Symphonia
Eternal Darkness
Skies of Arcadia: Legends
Beyond Good & Evil (multiplat)
Fire Emblem: Path of Radiance
Soul Calibur II

Wow, thanks so far! ;)

Okay, I´m definitely interested in:

- Tales of Symphonia
- Resident Evil Remake
- Eternal Darkness
- Killer 7

I played Mario Kart, Animal Crossing and Soul Calibur 2 already. Just forgot to mention them.

Is Skies of Arcadia really that good? Chibi Robo sounds interesting, as well but I´m not sure if I will like it.

I think I´ll do a "most important games / franchises" article. Otherwise Metroid and Zelda would take 4 of the top 10 already, which would be silly.

If you guys have any ideas where I can get some of those games for cheap tell me. I´ll definitely look around at ebay and amazon.

@Zen: Well, the Gamecube was mainly my "Nintendo console". I mostly played Nintendo games on it and bought some other games for PS2, but not that much, as well. I´m just not that much of a hardcore gamer anymore

Edit: @ Benga: I guess I´ll buy Fire Emblem for Wii so I won´t buy the GC game if it´s not really one of the best games on the Cube. (I want the most important games, as well in my list and Fire Emblem wasn´t that succesfull, as far as I know)

Hell, I was never interested in Skies of Arcadia... maybe I should give it a try?  

Louie:

I wouldn't have mentioned Fire Emblem if I thought it wasn't good. It is one of the hardest games of the previous generation. It's definitely an outstanding game in the Gamecube library. Successful is not the same as important. It was the first console Fire Emblem that was released outside Japan.

Skies of Arcardia is one of 3 good RPG's on Cube, despite being a Dreamcast port. You could save yourself the money of Final Fantasy, it's not very good. The definitive RPG is ToS.

Metroid 2 wasn't nearly as good as 1, so could be left from the list. Twilight Princess is more a Wii game, at least it wasn't important for Cube.

Get everything in Green.

EDIT:

Cult-classics:

-Viewtiful Joe.

-Eternal Darkness.

-Beyond Good and Evil.

-Baten Kaitos.

-Ikaruga.

-Skies of Arcadia: Legends.

-Killer7. 

Yeah, that´s quite a big list, thanks

I´ll work together with Benjamin on the article to get a better picture of the GC library.

Oh, yeah, I totally forgot about Baten Kaitos. I loved that game, even though it didn't do that well. If you have the chance, you should definitely pick it up. Battle system is great.

 No offense, but you really don't sound well equipped to do a "Best Of" GameCube article. It also seems you're judging a game's quality and importance on whether something is a "hit" or not(at least partially). Another clue would be that you seem very doubtful about the Skies of Arcadia mention, despite this game being praised for years on many forums. And the fact that you are completely ignoring Star Wars: Rogue Squadron II, a game that not only met your criteria for sales success, but also set the bar pretty high for the GC on a technical level.

Try doing a "Louie's Faves" type of article. An actual "Best Of..." article that doesn't hold water will be torn to shreds by any reasonable person, forget about fanboys going nuts on it. Maybe try doing an article like.....hmmmm...."Unfinished Journey: Exploring the GC Library". That would be very much in line with your experience with the Cube. You just don't have enough experience, or breadth of experience, on the Cube to do a definitive article on it's library.

 BTW, I'm still bothered by how you think a game must be a hit to be considered important for a console. Not being a tool, just stating mu concerns.

Oh yeah Wave Race Blue Storm is absolutely brilliant, in fact I think I would rate it my second favourite racer of all time (after F-Zero X)